Reliable long-range acoustic communications (LRAC) is an enabling technology for numerous applications of manned and unmanned underwater systems. For example, with the capability of communicating at long ranges of several hundreds or even thousands kilometers, it will become possible to remotely command and control unmanned underwater vehicles that are otherwise unreachable. As another example, underwater systems will be able to rely on such capability to establish a wide-area undersea network to complete missions in a collaborative fashion. As an active area of research, LRAC has received a tremendous amount of attention for the past two decades. A number of LRAC schemes have been proposed and tested by sea-going experiments. However, most research and experiments done so far have concentrated on the fixed LRAC cases where both the source and the receiver are moored (see e.g., M. Stojanovic, J. A. Catipovic, and J. G. Proakis, “Adaptive multichannel combining and equalization for underwater acoustic communications,” Journal of the Acoustical Society of America, vol. 94, no. 3, pp. 1621-1631, 2000; V. Capellano, “Performance improvements of a 50 km acoustic transmission through adaptive equalization and spatial diversity,” in OCEANS, October 1997, pp. 569-573; L. Freitag and M. Stojanovic, “Basin-scale acoustic communication: A feasibility study using tomography m-sequences,” in OCEANS, 2001. MTS/IEEE Conference and Exhibition, vol. 4. IEEE, 2001, pp. 2256-2261; A. Plaisant, “Long range acoustic communications,” in OCEANS, October 1998, pp. 569-573; and H. Song, W. Kuperman, and W. Hodgkiss, “Basin-scale time reversal communications,” The Journal of the Acoustical Society of America, vol. 125, p. 212, 2009).
In mobile LRAC applications the source and/or the receiver move at a significant speed. LRAC is made difficult by a number of factors, including (but not limited to) low signal-to-noise ratios (SNRs) mainly caused by large transmission losses, significant Doppler shifts induced by relative source-receiver motion as well as environmental factors such as internal waves, and severe inter-symbol interference (ISI) due to large channel delay spread. While these performance-limiting factors exist in both fixed and mobile LRAC, they tend to be more pronounced and therefore more difficult to be dealt with in the mobile cases, making an already challenging LRAC problem even more challenging. While many of the existing LRAC schemes developed for the fixed cases might in theory work well in the mobile cases, only a few have been actually tested at sea-going experiments. Examples include single-carrier communications with linear channel equalization reported in H. Song, S. Cho, T. Kang, W. Hodgkiss, and J. Preston, “Long-range acoustic communication in deep water using a towed array,” The Journal of the Acoustical Society of America, vol. 129, no. 3, pp. EL71-EL75, 2011, and orthogonal frequency division multiplexing (OFDM) reported in T. Kang, H. Song, and W. Hodgkiss, “Long-range multi-carrier acoustic communication in deep water using a towed horizontal array,” The Journal of the Acoustical Society of America, vol. 131, no. 6, pp. 4664-4671, 2012.
Disadvantages of these prior art approaches include the need of complicated receiver processing such as phase/Doppler tracking and correction, channel estimation and tracking, channel equalization, and frequent performance outage due to unpredictable environmental fluctuations. It is therefore desirable to provide a method that minimizes such disadvantages.